At the present time there is a major problem in establishing and maintaining a constant concentration of drugs that are administered intravenously to maintain anaesthesia. It is known in general terms that to achieve a constant concentration of a drug in the arterial blood plasma it is necessary to administer a bolus dose of the drug to establish an initial level, followed by an infusion of the drug to maintain the level over a period of time. Methods used to date to implement this general idea are based on conventional pharmacokinetic analysis where predictions are made from studies based on the administration of single doses of a drug.
To use such methods it is first necessary to mathematically describe the loss from the body of a single dose of the particular drug. The single dose of the drug is administered to a subject and then samples of blood are drawn over a number of days in order to define the decay in the concentration of the drug in the blood plasma. Then, using the mathematical process of residuals or by nonlinear least-square regression analysis, one or more pairs of exponential coefficients are derived to describe the decay of the curve to the zero point at infinite time (see FIG. 1). A description of this method is provided in detail by Gibaldi, M. and Perrier, D., "Pharmacokinetics" Marcel Dekker Inc., New York, 1982, pp 433 and 475)
Also, from the elimination profile the clearance (Cl) of the drug by metabolism or excretion from the body may be obtained by: EQU Cl =dose/AUC
where the plasma concentration/time curve is integrated (AUC) for up to three days following the administration of the dose of the drug, again see Gibaldi and Perrier, p. 321.
Once the coefficients of the decay curve and the clearance of the drug have been determined, it then becomes possible using mathematical transforms to create a mathematical model which simulates the distribution and elimination of the single dose of the drug. The model consists of compartments described in terms of their volume (eg. V1, V2 and V3) and rate constants (eg. k12, k21, k13, k31 and k10) for the movement of drug to and fro between the compartments (see (FIG. 2). The loss of drug from the system by detoxification or excretion is described either by an elimination rate constant or by the clearance of the drug from the particular patient. Such methods are fully described in many tests, particularly by Gibaldi and Perrier at pp 45-111.
Once such a mathematical model of the subject has been created it then becomes possible to design infusion patterns in an attempt to achieve a steady concentration.
Earliest methods of infusion have involved the injection of a single dose of the drug followed by a constant rate infusion. The infusion is used to counteract loss of drug by elimination while the single dose, based on the amount of drug required either, to reach the desired concentration in the initial volume of distribution (V1 in FIG. 2) or in the steady state volume of distribution (V1 +V2+V3 in FIG. 2), is used to establish an initial concentration. Both these methods however ignore the time related movement of drug between the compartments and have proved unsatisfactory for many drugs, particularly anaesthetic drugs which are lost rapidly from the circulation. The situation is compounded further for many anaesthetic drugs as they have very narrow ranges of safety making it highly desirably to hold concentrations close to that desired by the operator.
Various approaches have been described in an attempt to overcome the problem of rapid loss of drug to the tissues and the consequent, highly undesirable, fluctuations in blood concentration. Some involve either substitution of a short term loading infusion for the initial bolus or alternatively the addition of a smaller loading infusion to the bolus and maintenance doses.
The most popular methods of infusion, however, utilize the coefficients of the compartmental model (FIG. 2) derived using the methods outlined above and averaged for a number of patients to derive exponential infusions. The parameters of the model are used as a basis for calculating an infusion profile which will keep the concentration constant in the central compartment of the model on the assumption that the patient will behave as the model. Such a method results in a mono- or polyexponentially decaying infusion profile asymptoting to a constant rate which relates to the anticipated constant rate of elimination of the drug at a steady plasma concentration. The constant rate (assymptote) varies considerably between drugs, being determined by the ability of the patient to detoxify or excrete the drug. Such methods combining bolus, exponential decaying infusion and maintenance rate infusion have been described in theory by Kruger-Thiemer, E. in "Continuous intravenous infusion and multicompartment accumulation" in European Journal of Pharmacology, pp 317-324, Volume 4, (1968) and by Vaughan, D. P. and Tucker, G. T. in "General derivation of the ideal intravenous drug input required to achieve and maintain a constant plasma drug concentration. Theoretical application to lignocaine therapy." in European Journal of Clinical Pharmacology, pp 433-440, Volume 10, 1976.
A practical use of the exponential method, in particular the use of a computer to perform the required transforms and control the rate of a drug delivery device, has been described by Schwilden H., Schuttler J., Stoeckel H. G. and Lauven P. M. in "Strategies of Infusion for Intravenous Anaesthesia" in Pharmacological Basis of Anesthesiology, eds Tiengo M. and Cousins M. J., Raven Press, 1983. These authors describe a method where it is necessary to store in the memory of a computer averaged kinetic data, ie. the compartmental parameters shown in FIG. 2, for each drug as well as appropriate programs to perform the considerable mathematical operations required. Then, prior to an infusion, the operator nominates the concentration required in the plasma of the subject. Then by a method, of the type described by Kruger-Theimer, an infusion pattern is computed as time passes, the magnitude of which is used to control the rate of a drug delivery device.
Various other approaches to the generation of exponential infusions have been described which use pneumatic or electrical means. One such method is described by Stoffregen (German Patent Application DE No. 3227518 A1 - 24 July, 1981) which produces a mono-exponential decay. This method while apparently novel in electronic technique uses the well known exponential method and further does not appear to offer any means of generating a polyexponential decay. Also the method does not describe any means of adapting the infusion rate to achieve a nominated arterial plasma concentration of the drug or to vary the base rate of infusion in accordance with rate of elimination of the particular drug in use.